In this paper, using the Sobol sensitivity analysis method, which is based on variance, 11 factors affecting the optimization of the loading path of the hydroforming process are investigated, then the feasibility and validation of the results with other optimization methods such as finite element and experimental method are reported. Is Input factors include, expansion pressure, final pressure, yield time, end of expansion time, intermediate mandrel displacement, final mandrel displacement, intermediate mandrel displacement time, initial position of reciprocating mandrel, final position of reciprocating mandrel, start time of reciprocating mandrel and time The stops of the reciprocating mandrels are considered, then the effect of each of them on the minimum thickness and maximum height in the loading path of the hydroforming process to produce T-joints is investigated and reported in detail. Quantitatively and qualitatively, the optimal values are obtained for each of the 11 input factors and are calculated based on the loading paths.